I'm not sure you'll get a meaningful consensus to a question like this - lots of opinions maybe, which may or may not match your own iwhen you try them for yourself!
For what it's worth, my basses have radii (?) ranging from vintage 7.25" through 10", 16" and 20" to completely flat (ACG, Prose). The ACG also has an assymetric neck profile.
When I bought the ACG there were definitely a few converts out there who swore by the flat board and assym neck profile. I love my ACG but I've not been converted as such. I feel equally at home on my other regular necks.
A mild annoyance with smaller radius necks is sometimes a bit of string imbalance with flat pole pickups (G and E being closer to the poles). Smaller radius also requires more fiddling to get a low action, particularly on a tapered jazz type neck (P type generally not a prob).
It's easier IMO to set up a flat board with low action and even string balance. It's also easier to do DIY maintenance such as fret/fingerboard levelling. Not that I do a lot of that (although I have done some).
I can take or leave assymetric back-of-neck profiles. If pushed, I think I prefer a regular shallow C type profile. Maybe I'm just old fashioned. Having said that, my '57 P has the deepest V neck profile you could imagine and I love it to bits.
As with all this stuff, in the end it's largely down to personal foibles and preference!